Can This No. 4 Barrel Be Saved? (Or Is It Me...)

[ssgross]

Third photo is rust scale IMHO.

Could be dingy colored oil too. Appears to have a slight translucence to it.
If it is surface rust, boiling in plain old water will convert it to magnetite (bluing). Then again, with so little - shoot your rifle and it will go away Then care for it so it won't return. Take a pick with a birds eye (take the mirror off) of you new camera. If it's oil or grease, it will show up in different shades as you wipe a patch over it. If it's tarnished copper, it will show a dull but solid brown/orange. If it's rust, it will be a solid spot of dark brown. Carbon doesn't really show in the birds eye angle - shows black with the mirror, along with burnt on oil from firing.

Anyone every try Evaporust on a barrel? Works wonders on old motorcycle parts to remove the rust.

I've used it on parts before prepping for slow rust bluing before when going for an "antiqued" slow-rust blue effect. It will remove any and all bluing from anywhere it touches, even the accidental drop. I would never uses it if I cared to preserve anything left of the original finish. Boiling in water if you want preserve/conserve is the way to go. Lots of videos out there on this - a YouTube channel of "Anvil" by Mark Novak comes to mind. Cheaper than a jug of evaporust too - rain gutter section with end caps, a bit of jb weld to make the ends water tight, put it on your BBQ, in a bonfire, propane burner, whatever you got. Only need to boil 1-2 gallons of water to get the job done. Use a soft wire carding brush from Brownells (I think it's like $12 when I got mine, $25 for the very soft carding wheel to put on your motor), or just plain 0000 steel wool. evapo-rust is like $50 for the gallon jug. Gutter, caps, and steel wool are much, much cheaper.
One thing though, I did not scroll back up to see if your rifle has any suncorite paint on the exterior. Not sure how that will fair with any of the recommendations so far. Watch Mark Novak's conservation video. You'll be amazed at what comes out of the process with no refinishing, just boiling.

[Surpmil]

Could be dingy colored oil too. Appears to have a slight translucence to it.

I expect he's already run a brush down the bore a few times.

[buckbrush]

I use 2 stroke synthetic engine oil for nasty bores. Wet the bore with patches, wait 20 minutes, scrub with plastic bore brush, patch clean. Repeat if nesasary.